$$U_{1125}(x, y) = \left(\frac{x \left(1 - \sqrt{1 - 4 y}\right)^{2}}{4 y^{2}} + 1\right)^{3}$$

$$T_{1125}(n, m, k) = \begin{cases}1&\text{if n=0,m=0} ,\ \\\frac{2 n {\binom{3 k}{n}} {\binom{2 m + 2 n - 1}{m}}}{m + 2 n} \end{cases} $$